A vector version of the fixed point theorem of cone compression and expansion for a sum of two operators

Abstract

In this work, we establish a vector version of fixed point theorem of cone compression and expansion for an expansive operator with constant \(h > 1\) perturbed by a \(k\)-set contraction when \(0 \leq k < h – 1\). We give the compression-expansion conditions on components to allow the nonlinear term of a system to have different behaviors both in components and in variables. An example is given to illustrate our theoretical result.

Authors

Lyna Benzenati
Bejaia University, Bejaia, Algeria

Karima Mebarki
Bejaia University, Bejaia, Algeria

Radu Precup
Babes-Bolyai University, Cluj-Napoca, Romania

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L. Benzenati, K. Mebarki, R. Precup, A vector version of the fixed point theorem of cone compression and expansion for a sum of two operators, Nonlinear Studies 27 (2020), no. 3, 563-575.

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Nonlinear Studies

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